On the approximation of Min Split-coloring and Min Cocoloring

Overview & Synopsis

We consider two problems, namely Min Split-coloring and Min Cocoloring, that generalize the classical Min Coloring problem by allowing to use not only stable sets but also cliques to cover all the vertices of a given graph. We prove the NPhardness of some cases. We derive approximation results for Min Split-coloring and Min Cocoloring in line graphs, comparability graphs and general graphs. This provides to our knowledge the first approximation results for Min Split-coloring since it was defined only very recently [13, 8, 9]. Also, we provide some results on the approximability of Min Cocoloring and comparisons with Min Split-coloring and Min Coloring.